Kerson Huang

Fragmentation of relativistic heavy ions

Abstract The “incoherent droplet model” is used to explain recent experiments on the fragmentation of 16O during high energy collision with a Be target. In the 16O rest frame the fragments have a universal iso tropic Gaussian momentum distribution, independent to the masses of the fragments. The half-width of the Gaussian is 〈p〉 ( A 3 n ) , where, A is the mass number of the nucleus, n is the total number of fragments, and 〈p2〉 is the mean square momentum of individual nucleons in the fragmenting nucleus.

Transition Temperature of a Uniform Imperfect Bose Gas

We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase K{sub 0}(na{sup 3}){sup 1/6} , where n is the density, a is the S -wave scattering length, and K{sub 0} is a constant given in the paper. This disagrees with all existing results, analytical or numerical. {copyright} {ital 1999} {ital The American Physical Society }

Fixed point structure of scalar fields

We search for alternatives to the trivial {phi}{sup 4} field theory by considering nonpolynomial potentials. Such theories are renormalizable when the natural cutoff dependences of the coupling constants are taken into account. We find a continuum of fixed points, which includes the well-known Gaussian fixed point. The fixed-point density has a maximum at a location corresponding to a theory with a Higgs boson mass of approximately 2700 GeV. The Gaussian fixed point is UV stable in some directions in the extended parameter space. Along such directions we obtain nontrivial asymptotically free theories.

Nontrivial directions for scalar fields

We study the eigenvectors of the renormalization-group matrix for scalar fields at the Gaussian fixed point, and find that there exist {open_quote}{open_quote}relevant{close_quote}{close_quote} directions in parameter space. They correspond to theories with exponential potentials that are nontrivial and asymptotically free. All other potentials, including polynomial potentials, are {open_quote}{open_quote}irrelevant,{close_quote}{close_quote} and lead to trivial theories. Away from the Gaussian fixed point, renormalization does not induce derivative couplings, but it generates nonlocal interactions. {copyright} {ital 1996 The American Physical Society.}

PHONONS IN LIQUID HELIUM

Abstract By writing a dispersion relation for the density propagation function we obtain its most general form consistent with known sum rules, for any macroscopic system of bosons or fermions. The Fourier transform of the pair correlation Sk appears explicitly in the dispersion relation. An inequality for Sk is derived for any macroscopic system. We specialize the results to liquid He4 by making the single assumption that for k → 0, Sk “saturates” the inequality. This assumption is consistent with experiments and is later proved theoretically. The nature of the low-lying excited states of He4 can then be deduced. The result is that for given small momentum k, there is a group of states having an energy distribution peaked about ck, with a Lorentzian shape. The constant c is the velocity of sound at absolute zero, defined in terms of the macroscopic compressibility. The wave functions of these states are in some average sense Feynmans phonon wave function. We prove the assumption mentioned above by assuming Bose-Einstein condensation and by making essential use of the gauge invariance associated with the conservation particles. The mathematical technique is simple and does not require perturbation expansions, or summation of diagrams.

Fate of a Bose-Einstein condensate with an attractive interaction

We calculate the decay amplitude of a harmonically trapped Bose-Einstein condensate with attractive interaction via the Feynman path integral. We find that when the number of particles is less than a critical number, the condensate decays relatively slowly through quantum tunneling. When the number exceeds a critical one, a {open_quotes}black hole{close_quotes} opens up at the center of the trap, in which density fluctuations become large due to a negative pressure, and inelastic collisions will drain the particles from the trap. As the black hole is fed by tunneling particles, we have a novel system in which quantum tunneling serves as a hydrodynamic source. {copyright} {ital 1999} {ital The American Physical Society}

EXACT BOOTSTRAP SOLUTIONS IN SOME STATIC MODELS OF MESON-BARYON SCATTERING

We study the exact bootstrap solutions to four well‐known models of meson‐baryon scattering in the nonrecoil, one‐meson approximation. The models are the neutral scalar theory, the charged scalar theory, the symmetric scalar theory, and the neutral pseudoscalar theory. A bootstrap solution is defined to be a solution satisfying Levinsons theorem of potential scattering. It is found that the existence of a bootstrap solution depends crucially on the high‐energy conditions, which enter the problem through a cutoff function and through subtractions in the dispersion relations. In all the models considered there is no bootstrap solution with no subtraction. With one subtraction there exists more than one bootstrap solution. However, the requirements that (a) the meson‐baryon coupling constant should be different from zero, and (b) there should be no inelastic threshold below the elastic threshold, render the bootstrap solution unique. Positions of bound states and their coupling constants depend on two arbitrary parameters, which may be taken to be the cutoff momentum and the subtraction constant.

Capture ofμ−Mesons by Protons

By use of a two-component theory of the neutrino, the capture process and the radiative capture process of a mu /sup -/ by a proton is analyzed in some detail. (auth)

CAPTURE OF

By use of a two-component theory of the neutrino, the capture process and the radiative capture process of a mu /sup -/ by a proton is analyzed in some detail. (auth)

mu

The purpose of this work is to use a renormalized quantum scalar field to investigate very early cosmology, in the Planck era immediately following the big bang. Renormalization effects make the field potential dependent on length scale, and are important during the big bang era. We use the asymptotically free Halpern–Huang scalar field, which is derived from renormalization-group analysis, and solve Einstein’s equation with Robertson–Walker metric as an initial-value problem. The main prediction is that the Hubble parameter follows a power law: , and the universe expands at an accelerated rate: a ∼ exp t1 − p. This gives ‘dark energy’, with an equivalent cosmological constant that decays in time like t−2p, which avoids the ‘fine-tuning’ problem. The power law predicts a simple relation for the galactic redshift. Comparison with data leads to the speculation that the universe experienced a crossover transition, which was completed about seven billion years ago.